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An inverse mathematical technique for improving the sharpness of magnetic resonance images

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Abstract

Magnetic Resonance Imaging (MRI) is a powerful imaging modality with highly specific applications in medicine. However, certain series and sequences of MRI do not produce images with good acuity. Widely-used sharpening algorithms like Shock Filter (SF) and Unsharp Masking (UM) do not provide output images with appreciable sharpness-to-noise ratio. Output images of UM are prone to discontinuity artefact. A noise-robust sharpening algorithm to enhance acuity of MR images termed as Nonlinear Amplification of Spatial Derivative (NASD) that does not have the issue of discontinuity artefact is introduced in this paper. In the NASD, the enhanced image is estimated from the amplified spatial derivative in an inverse way. To avoid the amplification of noise, the amplification factor at any pixel location is calculated from a nonlinear function of the mean of the absolute values of the gradients along eight different orientations at that location. On hundred test images, the sharpness-to-noise ratio exhibited by NASD, SF and UM are 0.0963 ± 0.0400, 0.1642 ± 0.0967 and 0.2851 ± 0.1610. The computation time (in seconds) of NASD, SF and UM are 0.0330 ± 0.0031, 0.0452 ± 0.0390 and 0.0554 ± 0.0112. The NASD exhibits higher values of sharpness-to-noise ratio than SF and UM. NASD is able to sharpen the edges in the input image without amplifying noise and it is computationally fast like SF and UM.

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References

  • Aysal TC, Barner KE (2006) Quadratic weighted median filters for edge enhancement of noisy images. IEEE Trans Image Process 15(11):3294–3310

    Article  Google Scholar 

  • Bai Y, Jia H, Jiang M, Liu X, Xie X, Gao W (2020) Single image blind deblurring using multi-scale latent structure prior. IEEE Trans Circ Syst Video Technol 30(7):2033–2045

    Google Scholar 

  • Bhateja V, Misra M, Urooj S (2017) Human visual system based unsharp masking for enhancement of mammographic images. J Comput Sci 21:387–393

    Article  Google Scholar 

  • Bhateja V, Misra M, Urooj S (2018) Unsharp masking approaches for HVS based enhancement of mammographic masses: a comparative evaluation. Future Gener Comput Syst 82:176–189

    Article  Google Scholar 

  • Bhateja V, Nigam M, Bhadauria AS, Arya A, Zhang EY (2019) Human visual system based optimized mathematical morphology approach for enhancement of brain MR images. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-019-01386-z

    Article  Google Scholar 

  • Cherukuri V, Guo T, Schiff SJ, Monga V (2020) Deep MR brain image super-resolution using spatio-structural priors. IEEE Trans Image Process 29:1368–1383

    Article  MathSciNet  MATH  Google Scholar 

  • Coupé P, Yger P, Prima S, Hellier P, Kervrann C, Barillot C (2008) An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images. IEEE Trans Med Imaging 27(4):425–441

    Article  Google Scholar 

  • Guo J, He C, Wang Y (2020) Fourth order indirect diffusion coupled with shock filter and source for text binarization. Sig Procg 171:107478

    Article  Google Scholar 

  • Hardie RC, Boncelet CG (1995) Gradient-based edge detection using nonlinear edge enhancing prefilters. IEEE Trans Image Process 4(11):1572–1577

    Article  Google Scholar 

  • Ho KC, Speier W, Zhang H, Scalzo F, El-Saden S, Arnold CW (2019) A machine learning approach for classifying ischemic stroke onset time from imaging. IEEE Trans Med Imaging 38(7):1666–1676

    Article  Google Scholar 

  • Ibrahim H, Kong NS (2009) Image sharpening using sub-regions histogram equalization. IEEE Trans Consum Electron 55(2):891–895

    Article  Google Scholar 

  • Jeon G (2017) Computational intelligence approach for medical images by suppressing noise. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-017-0627-9

    Article  Google Scholar 

  • Jiao Z, Ji Y, Gao P, Wang SH (2020) Extraction and analysis of brain functional statuses for early mild cognitive impairment using variational auto-encoder. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-020-02031-w

    Article  Google Scholar 

  • Joseph J, Anoop BN, Williams J (2019) A modified unsharp masking with adaptive threshold and objectively defined amount based on saturation constraints. Multimed Tools Appl 78:11073–11089

    Article  Google Scholar 

  • Jung CR, Scharcanski J (2009) Sharpening dermatological color images in the wavelet domain. IEEE J Sel Top Sig Process 3(1):4–13

    Article  Google Scholar 

  • Krasula L, Callet PL, Fliegel K, Klíma M (2017) Quality assessment of sharpened images: challenges, methodology, and objective metrics. IEEE Trans Image Process 26(3):1496–1508

    Article  Google Scholar 

  • Lian C, Liu M, Zhang J, Shen D (2020) Hierarchical fully convolutional network for joint atrophy localization and alzheimer’s disease diagnosis using structural MRI. IEEE Trans Pattern Anal Mach Intell 42(4):880–893

    Article  Google Scholar 

  • Liu X, Tanaka M, Okutomi M (2013) Single-image noise level estimation for blind denoising. IEEE Trans Image Process 22(12):5226–5237

    Article  Google Scholar 

  • Liu S, Zhao C, Liu M, Xin Q, Wang SH (2019) Diffusion tensor imaging denoising based on Riemann nonlocal similarity. J Ambient Intell Human Comput 19:1–4

    Google Scholar 

  • Lyu Q, Shan H, Wang G (2020) MRI super-resolution with ensemble learning and complementary priors. IEEE Trans Comput Imaging 6:615–624

    Article  Google Scholar 

  • Narmatha C, Eljack SM, Tuka AA, Manimurugan S, Mustafa M (2020) A hybrid fuzzy brain-storm optimization algorithm for the classification of brain tumor MRI images. J Ambient Intell Human Comput 14:1–9

    Google Scholar 

  • Osher S, Rudin LI (1990) Feature-oriented image enhancement using shock filters. SIAM J Numer Anal 27(4):919–940

    Article  MATH  Google Scholar 

  • Paul J, Sivarani TS (2020) Computer aided diagnosis of brain tumor using novel classification techniques. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-020-02429-6

    Article  Google Scholar 

  • Rajan J, Poot D, Juntu J, Sijbers J (2010) Noise measurement from magnitude MRI using local estimates of variance and skewness. Phys Med Biol 55(16):N441

    Article  Google Scholar 

  • Rundo L, Tangherloni A, Nobile MS, Militello C, Besozzi D, Mauri G, Cazzaniga P (2019) MedGA: a novel evolutionary method for image enhancement in medical imaging systems. Expert Syst Appl 119:387–399

    Article  Google Scholar 

  • Schavemaker JG, Reinders MJ, Gerbrands JJ, Backer E (2000) Image sharpening by morphological filtering. Pattern Recognit 33(6):997–1012

    Article  Google Scholar 

  • Simi VR, Edla DR, Joseph J, Kuppili V (2019) Analysis of controversies in the formulation and evaluation of restoration algorithms for MR Images. Expert Syst Appl 135:39–59

    Article  Google Scholar 

  • Simi VR, Edla DR, Joseph J, Kuppili V (2020) Parameter-free fuzzy histogram equalisation with illumination preserving characteristics dedicated for contrast enhancement of magnetic resonance images. Appl Soft Comput 5:106364

    Google Scholar 

  • Torrents-Barrena J, Piella G, Masoller N, Gratacós E, Eixarch E, Ceresa M, Ballester MÁ (2019) Fully automatic 3D reconstruction of the placenta and its peripheral vasculature in intrauterine fetal MRI. Med Image Anal 54:263–279

    Article  Google Scholar 

  • Umer S, Rout RK, Pero C (2021) Facial expression recognition with trade-offs between data augmentation and deep learning features. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-020-02845-8

    Article  Google Scholar 

  • Vu CT, Phan TD, Chandler DM (2011) S3: a spectral and spatial measure of local perceived sharpness in natural images. IEEE Trans Image Process 21(3):934–945

    Article  MATH  Google Scholar 

  • Xiao J, Pang G, Zhang Y, Kuang Y, Yan Y, Wang Y (2016) Adaptive shock filter for image super-resolution and enhancement. J vis Commun Image Represent 40:168–177

    Article  Google Scholar 

  • Yu L, Zhang D, Peng N (2021) Research on the application of binary-like coding and Hough circle detection technology in PCB traceability system. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-020-02655-y

    Article  Google Scholar 

  • Zhang B, Allebach JP (2008) Adaptive bilateral filter for sharpness enhancement and noise removal. IEEE Trans Image Process 17(5):664–678

    Article  MathSciNet  Google Scholar 

  • Zhu X, Milanfar P (2010) Automatic parameter selection for denoising algorithms using a no-reference measure of image content. IEEE Trans Image Process 19(12):3116–3132

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology, Ponda, Goa, 403401, India

    V. R. Simi & Damodar Reddy Edla

  2. School of Bioengineering, VIT Bhopal University, Bhopal, Madhya Pradesh, 466114, India

    Justin Joseph

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  1. V. R. Simi
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  2. Damodar Reddy Edla
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  3. Justin Joseph
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Correspondence to V. R. Simi.

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Simi, V.R., Edla, D.R. & Joseph, J. An inverse mathematical technique for improving the sharpness of magnetic resonance images. J Ambient Intell Human Comput 14, 2061–2075 (2023). https://doi.org/10.1007/s12652-021-03416-1

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  • DOI: https://doi.org/10.1007/s12652-021-03416-1

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